Rebecca Murga always dreamed of working in Hollywood. But “when you’re poor and Puerto Rican, you don’t become a director,” she says. So Ms. Murga joined the military instead.

She was deployed in 2007, and served in Iraq, Afghanistan, and Kuwait. Murga is still an Army Reserve captain. But in addition to her military service, she’s recently become the first member of the military to be accepted into the American Film Institute Conservatory Directing Workshop for Women.

Hollywood, with its vocal critics of the wars in Iraq and Afghanistan, and the military may seem strange bedfellows. But the technical skills and rigorous discipline the military demands can prove to be beneficial when finding one’s way in the ultracompetitive world of film and television.

“[I]f I can live through a war, I can live through Hollywood,” says Murga, who hopes to one day add her name to the shortlist of female Hollywood directors. (Of the 250 highest-grossing films in 2014, only 7 percent were directed by women.)

Comedian Jon Stewart made headlines last spring when he revealed that he offers a five-week program to help veterans break into the TV industry. Others are helping vets make connections as well. Murga credits the organization Veterans in Film & Television for her start when she arrived in California in 2012 knowing no one. “There’s somewhat of a camaraderie,” she says of VFT. “It’s a place you can find support from other veterans. You’re a part of each other’s achievements.”

Through VFT she gained access to a range of role models and guest speakers, including production manager Dara Weintraub, whose credits include “Mad Men” and “Pineapple Express.” “Seeing women like that is confidence-building [for me],” Murga says.

Karen Kraft, a VFT board member and Army Reserve veteran, agrees. “They are excited for each other and supportive of each other,” she says of the nearly 2,000 members that make up VFT. “That military teamwork really comes out.”